In this specific case, the following answers both your concerns:
- Use
% at the end of each \stackrel to avoid a spurious space inserted by the new line (or carriage return) from your editor (you may only want to insert these between the entries you want to "keep together");
- Use
\strut in each element to raise the contents to a common level. Note that \strut, defines as \rule[-.3\baselineskip]{0pt}{\baselineskip}, accommodates for regular character descenders by virtue of a large enough depth and height.

\documentclass{article}
\usepackage{stackrel}% http://ctan.org/pkg/stackrel
\begin{document}
$\stackrel[\strut\textrm{3}]{\strut\textrm{1}}{\strut\textrm{2}}$
$\stackrel[\strut\textrm{sand}]{\strut\textrm{A}}{\strut\textrm{B}}$%
$\stackrel[\strut\textrm{wiches.}]{\strut\textrm{C}}{\strut\textrm{D}}$%
$\stackrel[\strut\textrm{E}]{\strut\textrm{rain}}{\strut\textrm{F}}$%
$\stackrel[\strut\textrm{G}]{\strut\textrm{cloud}}{\strut\textrm{H}}$%
$\stackrel[\strut\textrm{I}]{\strut\textrm{J}}{\strut\textrm{snow}}$%
$\stackrel[\strut\textrm{K}]{\strut\textrm{L}}{\strut\textrm{shoe}}$
$\stackrel[\strut\textrm{jones}]{\strut\textrm{M}}{\strut\textrm{N}}$%
$\stackrel[\strut\textrm{soda}]{\strut\textrm{O}}{\strut\textrm{P}}$%
$\stackrel[\strut\textrm{Q}]{\strut\textrm{yams}}{\strut\textrm{R}}$%
$\stackrel[\strut\textrm{S}]{\strut\textrm{yummy}}{\strut\textrm{T}}$%
$\stackrel[\strut\textrm{U}]{\strut\textrm{V}}{\strut\textrm{gummy}}$%
$\stackrel[\strut\textrm{W}]{\strut\textrm{X}}{\strut\textrm{bears}}$
$\stackrel[\strut\textrm{3}]{\strut\textrm{1}}{\strut\textrm{2}}$
\end{document}
An alternative, instead of using \stackrel, could just be to insert the contents in a tabular via a macro. Then the (vertical) alignment should be established by default. Here's a minimal example showing how that can be achieved:

\documentclass{article}
\newcommand{\stackitem}[3]{%
\begin{tabular}{@{}c@{}}#1\\#2\\#3\end{tabular}%
}
\begin{document}
\stackitem{A}{B}{sand}%
\stackitem{C}{D}{wiches.}%
\stackitem{rain}{F}{E}%
\stackitem{cloud}{H}{G}%
\stackitem{J}{snow}{I}%
\stackitem{L}{shoe}{K}
\end{document}
You'll notice that this provides the \stackrel functionality in a more convenient form since the order of the specified items follow the sequence they're displayed (left-to-right -> top-down). Also, it doesn't require the mathmode-textmode switching.
If you're interested in a more spread out display, that is easily obtainable by using, for example,
\renewcommand{\arraystretch}{2}%
which stretches out the rows by a factor of 2.
\stackrel) solution presents a new problem: if there are many\stackrel's, the document does not know when to break the line, so they run off the edge of the page. The second (tabular) solution will probably introduce too many other problems into my document. – Village Nov 16 '11 at 06:53tabularapproach introduce? Switching to/from math/text is not necessary in this case, and removes from your code readability. It seems like you're using thestackrelpackage just because it provides the stacking functionality while other, more suitable, alternatives exist. – Werner Nov 16 '11 at 07:26stackrelonly because it allows 3 levels of text. The stacks sometimes appear within the table of contents and inside\sectiontitles and sometimes contain\footnote's,\glossaryentries, cross-references of various kinds, etc. – Village Nov 16 '11 at 07:38strutused together withstackrel: if the word at the top has a lower-case "y", "p", "g", or "j" (which normally hang down below the line), then these words are pushed up. In other words, the bottom of "j" in "jump" will appear at the same hieght as the bottom of "z" in "zebra". – Village Nov 22 '11 at 00:00\stackrelexample in my post. There is no problem with the descenders in that case, since they line up properly across\stackrels, and there is no artificial height adjustments introduced. If this is not the case with your working example, then you need to post more information. – Werner Nov 22 '11 at 00:33strut's on every level. That pushes text away below and pushes text away above (at each line)? – Village Nov 22 '11 at 01:28